$ -1.\overline{4} \div 0.\overline{15} = {?} $
First convert the repeating decimals to fractions. $\begin{align*} 10x &= -14.4445...\\ x &= -1.4445...\end{align*} $ $\begin{align*} 9x &= -13 \\ x &= -\dfrac{13}{9}\end{align*} $ $\begin{align*} 100y &= 15.1515...\\ y &= 0.1515...\end{align*} $ $\begin{align*} 99y &= 15 \\ y &= \dfrac{15}{99}\end{align*} $ So, the problem becomes: $ -\dfrac{13}{9} \div \dfrac{15}{99} = {?} $ Dividing by a fraction is the same as multiply by the reciprocal of that fraction. $ -\dfrac{13}{9} \times \dfrac{99}{15} = {?} $ $ \phantom{-\dfrac{13}{9} \times \dfrac{15}{99}} = \dfrac{-13 \times 99}{9 \times 15} $ $ \phantom{-\dfrac{13}{9} \times \dfrac{15}{99}} = \dfrac{-13 \times \cancel{99}11} {\cancel{9} \times 15} $ $ \phantom{-\dfrac{13}{9} \times \dfrac{15}{99}} = -\dfrac{143}{15} $